Backers of expanded background checks for gun buyers have few quick options after their loss in the Senate.

WASHINGTON — Supporters of stricter gun laws have organization, money and — after the Senate blocked an expansion of background-check requirements — fury.

What they don't have is a clear path to changing the political arithmetic of the U.S. Congress.

None of next year's Senate races offers a good opportunity to replace a senator who backs gun rights with one who supports tougher laws.

Three senators who voted against expanding background checks face tough elections next year. All are Democrats from rural states that have strong gun-rights traditions: Sens. Mark Begich of Alaska, Mark Pryor of Arkansas and Max Baucus of Montana. If they lose, their replacements almost certainly would be pro-gun Republicans.

To find opportunities to switch a vote by defeating an incumbent senator, gun-control supporters may have to wait until 2016. Several Republican gun rights supporters face reelection that year in states where gun control has strong voter appeal; none fitting that description is on the ballot in 2014.

That electoral map belies some of the optimism for a fast turnaround that gun control supporters expressed after Wednesday's vote.

"Things change quickly here in Washington," said Sen. Charles E. Schumer (D-N.Y.). "They've changed for gay marriage. They're changing for immigration. And they will change for gun safety sooner than you think."

Schumer, however, has predicted such change before. "It will never be the same again. The vise lock that the NRA has had on the Senate and the House is broken," he once declared. That was in May 1999, after the Senate voted to close some gaps in the background-check law in response to the shootings a few weeks earlier at Columbine High School in Littleton, Colo. The measure failed in the House a month later.

The quickest cause of change might not be electoral defeats, but another shooting that shocks Americans.

"Next time a mass shooting happens — and if history is any guide, it will happen several times before November 2014 — every senator who voted against reform will be asked how they're feeling that morning," said Mark Glaze, executive director of Mayors Against Illegal Guns, the group co-founded by New York Mayor Michael R. Bloomberg that has provided much of the money behind gun control campaigns in the last year.

For now, the frustration bred by repeated defeats has helped generate a fissure in the alliance between advocacy groups and the Democratic leadership. Democrats have aimed to cast Wednesday's failure in partisan terms. President Obama did so in his speech just after the Senate vote, in which he cited polls showing that 90% of Americans support the idea of requiring all gun buyers to go through background checks.

"A few minutes ago, 90% of Democrats in the Senate just voted for that idea. But it's not going to happen because 90% of Republicans in the Senate just voted against that idea," he said.

Outside groups, by contrast, directed their ire across party lines on Thursday.

The most striking example came from Obama's own campaign operation, Organizing for Action, which announced it would mobilize supporters against both Democrats and Republicans who opposed the background-check plan.

"What is happening right now is the reason that OFA needs to be here: to harness the energy and determination of people," said the group's director, Jon Carson. "We need to show that the 90% on our side have staying power."

Similarly, the mayors group quickly posted on Twitter a graphic resembling a wanted poster featuring the four Democrats who voted no: Pryor, Baucus, Begich and Heidi Heitkamp of North Dakota. The title: "Meet the Soft on Crime Caucus."

For Democrats who bucked their party's stance on gun control, the biggest impact will probably be on their fundraising. Many large Democratic donors strongly support new gun laws.

On the other hand, in conservative states, being opposed by Obama's group and Bloomberg might help them, some political operatives said.